Category Archive for: Probability Statistics and Interpolation

Robot Path Control Using Three Knot Points Write a MATLAB program to compute the arm angle solution for three knot points. Write another program to compute the splines required to generate three knot points and to the path of the robot’s hand.Do this problem for the case where L, = 4, Lz = 3, =(6,O),(xf, yf)=(O,4) Solution The…

Statistical Analysis and Manufacturing Tolerances Suppose you must cut a triangular piece off the comer of a square plate by measuring the distances x and y from the comer (see Figure 7.3-2). The desired value of x is 10 in., and the desired value of () is 20°. This requires that y = 3.64 in. We are told…

Optimal Production Quantity You have recently taken a position as the engineer in charge of your company’s seasonal product, which is manufactured during the off-season. You want to determine the optimum production level. If you produce more units than you can sell, your profit will not be as large as it could be; if you produce too…

Estimation of Height Distribution Use the results of Example 7.2-1 to estimate how many 20-year-old men are no taller than 68 in. How many are within 3 in. of the mean? Solution In Example 7.2-1 the mean and standard deviation were found to be J-L = 69.3 in. and (1= 1.96 in. In Table. 7.2-1, note that…

Gauss Elimination Statistical analysis of data on human proportions is required in many engineering applications. For example, designers of submarine crew quarters need to know how small they can make bunk lengths without eliminating a large percentage of prospective crew members. Use MATLAB to estimate the mean and standard deviation for the height data given in Table 7.2-1. Solution…

Breaking Strength of Thread To ensure proper quality control, a thread manufacturer selects samples and tests them for breaking strength. Suppose that 20 thread samples are pulled until they break, and the breaking force is measured in newtons rounded off to integer values. The breaking force ‘values recorded were 92, 94, 93, 96, 93,:94, 95, 96, 91, 93,…

Problems You can find the answers to problems marked with an asterisk at the end of the text. The following list gives the measured gas mileage in miles per gallon for 22 cars of the same model. Plot the absolute frequency histogram and the relative frequency histogram 23 25 26 25 27 25 24 22 23 25 26 26…

Summary This chapter introduces MATLAB functions that have widespread and important uses in statistics and data analysis; however, their proper application requires informed judgment and experience. Section 7.1 gives an introduction to basic statistics and probability, including histograms, which are specialized plots for displaying statistical results. The normal distribution that forms the basis of many statistical…

Interpolation Engineering problems often require the analysis of data pairs. For example, the paired data might represent a cause and effect, or input-output relationship, such as the current produced in a resistor as a result of an applied voltage, or a time history, such as the temperature of an object as a function of time. Another type of paired…

We often do not have a simple probability distribution to describe the distribution of outcomes in many engineering applications. For example, the probability that a circuit. consisting of many components will fail is a function of the number and the .age’of the components, but we often cannot obtain a function to describe . the failure probability. In such cases…